Grade 10 Math: Inequalities and System of Equations
This worksheet covers solving linear inequalities, graphing solutions, and solving systems of linear equations using various methods.
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Grade 10 Math: Inequalities and System of Equations
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Solve the inequality and graph the solution on the number line: 3x - 5 < 10
2. Use the substitution method to solve the system of equations: y = 2x + 1 4x + y = 13 Substitute the first equation into the second: 4x + ( ) = 13 Simplify and solve for x: x = Substitute the value of x back into the first equation to find y: y = The solution is ( , ).
3. The graph of y > 2x - 3 will have a dashed line and the region above the line shaded.
True
False
4. Which of the following systems of equations would be best solved using the elimination method? A) y = 3x - 2; x + y = 8 B) 2x + 3y = 7; 2x - 5y = 15 C) x = 5y + 1; 3x - 2y = 10 D) x + y = 4; x - y = 0
A
B
C
D
5. Graph the solution set for the system of inequalities: y ≥ x - 2 y < -2x + 4
6. A local theater sells tickets for $10 for students and $15 for adults. On a particular night, 200 tickets were sold for a total of $2500. Write a system of equations to represent this situation and solve it to find out how many student tickets and adult tickets were sold.
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